\frac{1}{n - 1} + \frac{13}{12} - \frac{1}{24} \left(n - 1\right)^{2} + \frac{11}{720} \left(n - 1\right)^{3} - \frac{11}{1440} \left(n - 1\right)^{4} + \frac{271}{60480} \left(n - 1\right)^{5} + \frac{5 n}{12} + \mathcal{O}\left(\left(n - 1\right)^{6}; n\rightarrow 1\right)